Projectile Motion - Center of Mass

In summary, a rocket is launched from the ground with a speed of 18.0m/s and a direction of 51.0 above the horizontal. During its flight, it explodes into two pieces of equal mass. To determine the horizontal distance from the launch point where the center of mass of the two pieces will land, we can use kinematics equations. The final distance of the center of mass is calculated to be 32.4m. To find the landing point of the second piece, we need to use an equation that relates the positions of the two masses to the position of the center of mass.
  • #1
annastewert
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0

Homework Statement


In a fireworks display a rocket is launched from the ground with a speed of 18.0m/s and a direction of 51.0 above the horizontal. During the flight, the rocket explodes into two pieces of equal mass. What horizontal distance from the launch point will the center of mass of the two pieces be after both have landed on the ground? If one piece lands a horizontal distance of 26.0m from the launch point, where does the other piece land?

Homework Equations


Kinematics?

The Attempt at a Solution


I got 32.4m for the final distance of the center of mass, but I'm not sure what to do for the landing point of the second piece.
 
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  • #2
Find out the equation that tells you the pisition of the com from the positions of the two masses.
 

1. What is projectile motion?

Projectile motion is the movement of an object through the air or space under the influence of gravity. It follows a curved path known as a parabola.

2. What is the center of mass in projectile motion?

The center of mass in projectile motion is the point at which the entire mass of the object can be considered to be concentrated for the purposes of calculating its motion. In other words, it is the point where all the forces acting on the object can be considered to act through.

3. How is the center of mass related to the trajectory of a projectile?

The trajectory of a projectile is directly related to its center of mass. The center of mass determines the direction and speed of the projectile's motion, and therefore, the shape of its trajectory.

4. Can the center of mass of a projectile change during its motion?

Yes, the center of mass of a projectile can change during its motion if external forces, such as air resistance, act on the object. However, if there are no external forces, the center of mass will remain constant.

5. How is the center of mass calculated in projectile motion?

The center of mass can be calculated by taking the weighted average of the individual masses of the object. This is done by multiplying the mass of each part of the object by its distance from the chosen reference point, then dividing the sum of these values by the total mass of the object.

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